So in playing a variant of Rome total war, I noticed that the faction "Holy Roman Empire" all had German names, language, culture, etc. etc.
Is this even true or is my game just historically inaccurate?
I always assumed that the Roman Empire was based out of Rome and as such was Italian in culture, heritage, etc.
As mentioned elsewhere, the Holy Roman Empire and the Roman Empire are two different, unrelated entities. One was a classical age civilisation centred in Italy and the Mediterranean basin, whereas the other was a Germanic medieval and early modern "state". The name comes from the idea that the Holy Roman Emperor, crowned by the Pope, is the heir to the power and glory of the Roman Empire of antiquity.
So yes, your game is accurate in having the Holy Roman Empire have Germanic names, although the Holy Roman Empire did control significant portions of Italy at times too! In name at least, at its greatest extent the Empire included Germany--including Austria and Bohemia--the Low Countries, parts of what are now eastern France, along with Lombardy and Savoy in Italy. Rome itself, however, was generally within the Papal State, or territory ruled directly by the Pope. However, its focus was eventually shifted to its German lands, and the Empire was renamed to the "Holy Roman Empire of the German Nation".
The history of the Holy Roman Empire is fascinating, and it lated all the way up till when the last Emperor abdicated in the wake of Napoleon's conquests. The structure of the Holy Roman Empire was important for the way the Protestant Reformation played out, the outbreak of the Thirty Years War, and many other important events in European history. It's definitely something worth checking out.
The Roman Empire of Antiquity and the Holy Roman Empire are two unrelated entities, except for the fact that the Holy one claimed to be the successor of the other one.
When the Western Roman Empire fell in 476, the Eastern Roman Empire centered around Constantinople (today's Istanbul) continued to exist for another 1000 years. Despite this, Charlemagne, King of the Franks and Italy, was crowned Holy Roman Emperor by the Pope in 800.
In 936, the German king Otto was again crowned Holy Roman Emperor and he controlled what is today more or less Germany, Austria, Switzerland, the Netherlands and Northern Italy.
The various Emperors were elected by a handful of German princes and bishops and then crowned by the Pope. At some point, the Emperor was always the Archduke of Austria as well, up until the dissolution of the Holy Roman Empire in 1806 with the abdication of Francis II.
The history of the Holy Roman Empire, even in comprised form, can fill multiple books, and I suggest you read any of them.